Answer:
A) g(x)= 1/2(x-8)^2-8. The vertex is (8, -8).
Step-by-step explanation:
A. g(x)= 1/2(x-8)^2-8 is the vertex form of the function.
In general it can be written as
f(x) = a(x - h)^2 + k where (h, k) is the vertex.
Here the vertex is (8, -8)
For given function g(x), vertex = (8, -8)
The correct answer is option (A)
"The graph of the quadratic function is shaped like a parabola. The form of this quadratic function is called vertex form."
"The vertex of the graph of a quadratic function is the highest or lowest possible output for that function. "
For given example,
We have been given three equivalent forms of a quadratic function g.
[tex]g(x) = \frac{1}{2} (x-8)^2-8\\\\g(x) = \frac{1}{2}(x-12)(x-4)\\\\g(x) = \frac{1}{2}x^2-8x+24[/tex]
In general the vertex form of a function can be written as
f(x) = a(x - h)^2 + k,
where (h, k) is the vertex.
From these functions the function g(x)= 1/2(x-8)^2-8 is vertex type function.
Comparing with the general equation,
we have h = 8 and k = -8
So, the vertex are (8, -8).
The correct answer is option (A)
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